1/5 of the population cycle to work. If 2/3 of these cyclists ride mountain bikes, what fraction of the population cycle with mountain bikes to work?

Step-by-step explanation:Let's change the denominator of [tex] \frac{1}{5} [/tex]to 15 as it is the lowest common multiple of both denominators, 5 and 3. [tex] \frac{1}{5} = \frac{3}{15} [/tex]Now, think of it this way, there are 15 people cycling and [tex] \frac{1}{5} [/tex]of them cycle to work. [tex] \frac{1}{5} = \frac{3}{15} [/tex][tex] \frac{3}{15} \times 15 = 3[/tex]Out of these 15 cyclists, 3 of them go to work. As [tex] \frac{2}{3} [/tex]of these remainders cycle via mountain bikes, we can find how many people ride mountain bikes to work. [tex] \frac{2}{3} \times 3 = 2[/tex]As there was a total of 15 people at the start and 2 who rode mountain bikes to work, the fraction of the population who rides mountain bikes to work will be [tex]2 \div 15 = \frac{2}{15} [/tex]Short answer:[tex] \frac{1}{5} \times \frac{2}{3} = \frac{2}{15} [/tex]